from any point p outside a given circle, there are two lines through p that are tangent to the circle. explain why the distance from p to one of the points of tangency is the same as the distance from p to the other point of tangency. what special quadrilateral is formed by the center of the circle, the points of tangency, and p?

Answer:

The solution of the mathematical expressions will be 0.175.

Step-by-step explanation:

Given that;

The mathematical expressions are,

⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6

Now,

Solve the mathematical expression as;

⇒  [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6

Using the BODMAS rule to solve the expressions as;

⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6

⇒ [ 2 - | - 1/4 + 6/5 | ÷ -6

⇒ [ 2 - 19/20 ] ÷ -6

⇒  [ 21/20] ÷ -6

⇒ 21/20 x 1/-6

⇒ - 7 / 40

Therefore,

The solution of the mathematical expressions will be 0.175.

But you didn't have to cut me off

Make out like it never happened and that we were nothing (aah-ooh)

And I don't even need your love (ooh)

But you treat me like a stranger, and that feels so rough (aah)

No, you didn't have to stoop so low (ooh)

Have your friends collect your records and then change your number (aah)

I guess that I don't need that, though

Now you're just somebody that I used to know

Answer:

[tex]-\dfrac{7}{40}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left[2-\left|-\dfrac{1}{4}-2\left(-\dfrac{3}{5}\right)\right|\right] \div (-6)[/tex]

Carry out the operations inside the absolute value bars (following the order of operations):

[tex]\implies \left[2-\left|-\dfrac{1}{4}+\dfrac{6}{5}\right|\right] \div (-6)[/tex]

[tex]\implies \left[2-\left|\dfrac{19}{20}\right|\right] \div (-6)[/tex]

As the fraction inside the absolute value bars is already positive, we can simply remove the bars:

[tex]\implies \left[2-\dfrac{19}{20}\right] \div (-6)[/tex]

Rewrite 2 as 40/20 and carry out the subtraction inside the square brackets:

[tex]\implies \left[\dfrac{40}{20}-\dfrac{19}{20}\right] \div (-6)[/tex]

[tex]\implies \left[\dfrac{40-19}{20}\right] \div (-6)[/tex]

[tex]\implies \left[\dfrac{21}{20}\right] \div (-6)[/tex]

Rewrite -6 as a fraction:

[tex]\implies \dfrac{21}{20} \div -\dfrac{6}{1}[/tex]

When dividing fractions, multiply the first fraction by the reciprocal of the  second fraction:

[tex]\implies \dfrac{21}{20} \times-\dfrac{1}{6}[/tex]

[tex]\implies \dfrac{21 \times (-1)}{20 \times 6}[/tex]

[tex]\implies -\dfrac{21}{120}[/tex]

Reduce the fraction to its simplest form by dividing the numerator and denominator by the highest common factor, 3:

[tex]\implies -\dfrac{21 \div 3}{120 \div 3}[/tex]

[tex]\implies -\dfrac{7}{40}[/tex]

The value of (AB)² is 15.

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius. Two circles can be called congruent if they have the same radius. Equal chords are always equidistant from the center of the circle. The perpendicular bisector of a chord passes through the center of the circle. When two circles intersect, the line connecting the intersecting points will be perpendicular to the line connecting their center points. Tangents drawn at the endpoints of the diameter are parallel to each other.

Equation of first circle:

(x - 2)² + (y + 1)² = 4²

Equation of secnd circle:

(x - 2)² + (y - 5)² = (√10)²

Solve for (x - 2)² :

(x - 2)² + (y + 1)² = 4²   ==>   (x - 2)² = 16 - (y + 1)²

(x - 2)² + (y - 5)² = (√10)²   ==>   (x - 2)² = 10 - (y - 5)²

Then,

16 - (y + 1)² = 10 - (y - 5)²

16 - (y ² + 2y + 1) = 10 - (y ² - 10y + 25)

15 - 2y - y ² = -15 + 10y - y ²

30 - 12y = 0

12y = 30

y = 30/12 = 5/2

Thus, the y coordinate of A and B is 5/2.

Then solve for x :

(x - 2)² = 16 - (5/2 + 1)²

(x - 2)² = 15/4

x - 2 = ± √(15/4) = ±√15/2

x = 2 ± √15/2

Thus, the x coordinates for either A or B are 2 +√15/2 or 2- √15/2.

The intersections points are A = (2 - √15/2, 5/2) and B = (2 + √15/2, 5/2). Thus, the squared distance between them:

(AB)² = [(2 - √15/2) - (2 + √15/2)]² + (5/2 - 5/2)²

(AB)² = (-√15)² + 0²

(AB)² = 15

Thus, the value of (AB)² is 15.

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Answer:

5/4 should be the answer.

Step-by-step explanation:

2 divided by 8/5 = 5/4

Answer:

Step-by-step explanation:

x is 5/4

8x/5=2

8x=10

x=5/4

The probability that a junior bio major who has taken statistics has also taken a computer course is 13.46%.

We are trying to find the probability that a junior bio major who has taken a statistics course has also taken a computer course. This is referred to as the conditional probability, denoted as P(computer | statistics).

To calculate this, we can use the formula:

P(computer | statistics) = P(computer and statistics) / P(statistics)

This formula states that the probability of a junior bio major taking a computer course given that they have taken a statistics course is equal to the probability of them taking both a computer and statistics course divided by the probability of them taking only a statistics course.

The information given in the problem is as follows:

P(statistics) = 52%

P(computer) = 23%

P(computer and statistics) = 7%

So we can plug these values into the formula to calculate the conditional probability:

P(computer | statistics) = P(computer and statistics) / P(statistics) = 7% / 52% = 0.1346153846153846 or 13.46%

Therefore, the probability that a junior bio major who has taken statistics has also taken a computer course is 13.46%.

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The complete Question is:

A university requires its biology majors to take a course called BioRe search. The prerequisite for this course is that students must have taken either a Statistics course or a computer course. By the time they are juniors, 52% of the Biology majors have taken Statistics, 23% have had a computer course , and 7% have done both. What's the probability that a junior bio major who has taken statistics has also taken a computer course?

Variables are the name for the unknown.You must isolate the variable in order to get a solution for it (such as x).

Unknown value.Variables are the name for the unknown.You must isolate the variable in order to get a solution for it (such as x).

The variable can be separated from the equation by performing inverse operations.Adding and multiplying are the opposites of subtracting and dividing, respectively.

Starting with the proportion:

12/? = 4/3

Since it should be equal to 4/3, notice that if we divide both numerator and denominator by 3, then we should get 4 and 3 respectively:

Therefore, ?÷3 is equal to 3.

Which number is equal to 3 when we divide it by 3?

That number is 9. 9÷3=3

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Answer:

=x^2+1 (Graph Example), 4x+2=2 (x+6) (Solve Example) Algebra Calculator is a calculator that gives step-by-step help on algebra problems. See More Examples ». x+3=5. 1/3 +

Step-by-step explanation:

Answer:

y=x^2+1

Step-by-step explanation: 4x+2=2 (x+6)

We can see from the graph that Plan B is less expensive for the range [0, 4], however Plan A is superior if you watch 4 or more movies per month.

We know that plan A costs $14 per month plus $2 per movie, so if you watch x movies, the cost is:

C₁(x) = $14 + $2*x

Plan B costs $20 per month plus $1 per movie, so if you watch x movies, the cost is:

C₂(x) = $20 + $1*x

You can see in the graph that the blue line is behind the green one between x = 0 and x = 4. Plan B is therefore less expensive in the range [0, 4].

The green line is underneath the blue one for x > 4, hence you should select plan A for x > 4.

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The Hindu-Arabic numeral system is superior to other numeral systems because of its invention of the number 0. This allows for the representation of the concept of nothingness or absence, which allows for the development of more advanced mathematical operations such as negative numbers and decimal fractions.

The two purposes of numerals or digits are to show the cardinal value (how many) and to show the place value (10s, 100s, 1000s). The cardinal value is the actual quantity of a number, while the place value is the position of a digit in a number, which determines its value in relation to other digits.

The natural numbers are the numbers used in a counting process and do not include 0. They include the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on to infinity. The principle of closure is the idea that certain operations, such as addition and multiplication, will always result in a natural number when performed on natural numbers. However, subtraction and division do not result in natural numbers in all cases.

Integers are positive and negative numbers that start at 0 and expand infinitely in both directions. They are closed under addition, multiplication, and subtraction. However, division is not closed under integers.

Rational numbers are numbers that can be expressed as the quotient of two integers. Irrational numbers are non-terminating, non-repeating decimals.

The three axioms of equality are the reflexive property (A = A), the symmetric property (if A = B, then B = A), and the transitive property (if A = B and B = C, then A = C).

The commutative property states that the order of the numbers does not affect the result in operations such as addition and multiplication. The associative property states that the grouping of numbers does not affect the result in operations such as addition and multiplication. The distributive property states that multiplication can be distributed over addition.

The unity element for multiplication is the number 1, which serves as the identity element for multiplication. The zero element for addition is 0, which serves as the identity element for addition. Dividing by 0 is an error and not allowed.

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Using simple mathematical operations, we know that we can have 10 different arrangements to plant 2 apple trees and 5 pear trees in a row.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.

Parentheses, Exponents, Multiplication, and Division (from Left to Right),

Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).

So, we know that:

Golden delicious apple trees: 2

Bartlett pear tree: 5

Different arrangements that can be made are as follows:
2 * 5

10

Therefore, using simple mathematical operations, we know that we can have 10 different arrangements to plant 2 apple trees and 5 pear trees in a row.

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Answer:

A and D

Step-by-step explanation:

The Empirical Rule states that for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.

Given that the mean value of land and buildings per acre from the sample of farms is $1800 and the standard deviation is $300, we can use this information to determine which farms are unusual (more than two standard deviations from the mean).

A. $615 is unusual, it is more than two standard deviations from the mean, which is $1800. $615 is $1185 less than the mean. Since it is more than $600 less than the mean, it is more than two standard deviations from the mean.

B. $1656 is not unusual, it is less than 2 standard deviations from the mean.

C. $1625 is not unusual, it is less than 2 standard deviations from the mean.

D. $2493 is unusual, it is more than two standard deviations from the mean, which is $1800. $2493 is $693 more than the mean. Since it is more than $600 more than the mean, it is more than two standard deviations from the mean.

E. $1521 is unusual, it is more than two standard deviations from the mean, which is $1800. $1521 is $279 less than the mean. Since it is more than $600 less than the mean, it is more than two standard deviations from the mean.

F. $1664 is not unusual, it is less than 2 standard deviations from the mean.

None of the data values are very unusual (more than three standard deviations from the mean).

So the farms that are unusual (more than two standard deviations from the mean) are A and D.

Answer: Using the empirical rule, if the distribution is bell-shaped, we know that about 68% of the data falls within one standard deviation of the mean, about 95% of the data falls within two standard deviations of the mean, and about 99.7% of the data falls within three standard deviations of the mean.

To determine which of the farms are unusual (more than two standard deviations from the mean), we need to calculate the lower and upper bounds for two standard deviations from the mean:

Lower bound = Mean value - (2 * Standard deviation) = $1800 - (2 * $300) = $1200

Upper bound = Mean value + (2 * Standard deviation) = $1800 + (2 * $300) = $2400

So, any data value outside this range is considered unusual. Therefore, the farms that are unusual are:

$2493 (more than two standard deviation from the mean)

None of the data values are very unusual (more than three standard deviations from the mean)

Step-by-step explanation:

The experimenters would then plot the number of viruses per milliliter of culture on a graph over time.

This graph will show the rate of infection for each virus and the total amount of virus present in the culture at any given time. This data can then be used to compare the infectivity of the two viruses and any differences in their replication rates.

The experimenters infected cells with either virus A or virus B and then sampled the mixture at five-minute intervals. After removing the intact cells, the number of viruses per milliliter of culture was determined and plotted on a graph over time. This data can then be used to compare the infectivity of the two viruses and any differences in their replication rates.

The experimenters would then plot the number of viruses per milliliter of culture on a graph over time.

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Answer:

p

Step-by-step explanation:

no of dimes you have =17

no of dimes your brother have=8

now

no of dimes more you have save =17-8

=9

hence you have saved 9 more dimes

The bearing of H from P is 243°26′

In mathematics, an angle is a measure of the amount of rotation between two lines or planes. It is measured in units of degrees or radians. An angle is formed by two rays that have a common endpoint called the vertex. The rays are the sides of the angle and the vertex is the point where the rays meet.

An angle is defined by its measure, which is the amount of rotation between the two rays. The most common way to measure angles is in degrees, where a full rotation is equal to 360 degrees. Another way to measure angles is in radians, where a full rotation is equal to 2*pi radians.

Let the bearing of H from P be represented by x°.

tanθ=3060=0.5

θ=tan−1(0.5)=26.565°

x=180°+(90−26.565)

x=180+63.435=243.435°

= 243°26′

Hence, the bearing of H from P is 243°26′

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The main difference between the line segment and the directed line segment is given by line segment has two endpoints and the directed line segment has only one end point.

As given in the question,

Difference between the line segment and the directed line segment is given by following points:

Therefore, different number of endpoints represents the main difference between line segment and the directed line segment  given by :

line segment with two endpoints and directed with one end point.

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Length of the person's shadow is 3.75 feet.

Consider triangle as shown, segment DE represent the person standing, A represent the location of light, 22 feet away from ground, BC. The shadow's length would be the length of CE.

In triangle ABC and triangle DEC, ∠C is common, and ∠CBA = ∠CED = 90°. So by AA criterion, the triangles are similar. Thus

BC/ CE = AB/ DE

(BE + CE)/CE = AB/ DE

1 + BE/CE = AB/ DE

1 + 10/CE = 22/6

10/CE = 16/6 = 8/3

CE = (10 × 3)/8

CE = 3.75

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The information provided indicates that it will take 78 minutes to load.

Time may be described in mathematics as a continuing and continuous series of events that take place one after another, from the past through the present, and into the future. The length of events or the gaps between them may be measured, compared, or even ordered using time.

If loading three and a half trucks takes 42 minutes, loading one truck will take 42 / 3.5 minutes, or 12 minutes. The time needed to load is calculated by multiplying the minutes per vehicle by 6.5. In this scenario, it would take 78 minutes to load 6 1/2 trucks (12 x 6.5). The time taken is calculated using the formula t = 12n, where n indicates the number of trucks and t is the time in minutes.

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Answer:

t - 2 = the number of treats remaining.

Step-by-step explanation:

Answer:

Step-by-step explanation:

t-2

A integer, a constant, or a mix of both, combined with specific operation symbols, make up an expression 3r+ 37.5 is the equation.

A number, a constant, or a mix of both, combined with specific operation symbols, make up an expression. An expression can only be an exponential function if it contains both an operators and a variable. Any unknown term can be used as a factor, together with the operator + and -. Examples of such terms include x, y, and z. Since 5 isn't an exponential function, it can be claimed that it.

Here,

Given :

It is reasonable to assume that r = n rides. Since each ride costs $3 ($3xr), the total cost is $3.

In addition, we know that FIVE people, including Tory and every one of her friends, will be at the fair. The entrance fee is $7.50, therefore we can increase it by five to reach $37.5.

That is $3r plus $37.5.

Therefore, the equation is $37.5 + $3r, where r seems to be the total of rides taken by Tory and his friends.

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The solution to the system in given tables of line 1 and line 2, using linear equation is (b) (0,5)

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

from the table of line 1, the equation of line is

y = 2x +5.

from the table of line 2, the equation of line is

y = 5 - x

to find the solution of the system, we compare both of the equation, we get

2x + 5 = 5 - x

add x from both side, we get

3x + 5 = 5

subtract 5 from both side, we get

3x = 0

So that, x = 0

putting the value of x in the equation of line 2

y = 5 - x

y = 5 - 0

y = 5

The solution to the system in given tables of line 1 and line 2 is (0,5)

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Answer:

(1, 2)

Step-by-step explanation:

Looking at the graph, you can find the point of intersection. The point of intersection is over 1 on the x-axis, and next to 2 on the y-axis. So, the coordinate of the point of intersection is (1, 2).

Hope this helped!

Please give me brainliest if possible!

The gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1).

This gradient is a vector pointing in the direction of the function f(x, y, z) = log(x2 + y2 + z2 )'s rate of growth. Calculating the function's partial derivatives with respect to x, y, and z is necessary to assess this gradient.

The function's partial derivative with regard to x is (2x / (x2 + y2 + z2) This becomes 2/1 when x is 1. The partial derivative with regard to z is (2z / (x2 + y2 + z2)), which becomes 2/1 when z is 1, and the partial derivative with respect to y is 0, and the partial derivative with respect to z is 0, respectively. Therefore, at (1, 0, 1), the gradient of f(x, y, z) = log(x2 + y2 + z2) is (2/1, 0, 2/1).

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The point of partition of the line segment AB in the ratio 2:3 with endpoints at A(9,5) and B (4,-5) is (7,1) .

What is Partition ?

The Simple words Partition means to separate or to divide . and

we know that , the point of partition of the line segment AB in the ratio a:b , can be calculated using the formula :

[tex]P=\frac{bA+aB}{a+b}[/tex] ;

Substituting the values of end points A(9,5) and B (4,-5) and the ratio [tex]a=2[/tex] , [tex]b=3[/tex] ,

we get ;

P = [tex]\frac{3(9,5) +2(4,-5)}{2+3}[/tex] = [tex]\frac{(27,15) + (8,-10)}{5}[/tex] = [tex]\frac{(35,5)}{5}[/tex] ;

Simplifying further ,

we get ;

P = (7,1) .

Therefore , the point of partition P is (7,1) .

The given question is incomplete , the complete question is

How do I find the point that partitions the segment AB into a 2:3 ratio with endpoints at A(9,5) and B (4,-5) ?

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The required difference in time taken by bob and sam is 0.8 hour.

Speed is defined as. The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

Bob can drive 50 miles in 40 minutes.

So, Speed of bob = 50×60/40 = 75 miles/hour

And Sam can drive 90 miles in 105 minutes.

Speed of Sam = 90×60/105 = 51.4 miles/hour

Now/

Time taken by bob(d) = 120/75 = 1.6

Similarly,

Time taken by Sam(e) = 120/51.4 = 2.4

So,

d - e

|1.6 - 2.4|

0.8

Thus,required difference in time is 0.8.

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keeping in mind that a centroid cuts all medians at a 2 : 1 ratio, meaning that the median AE gets cut on a 2 : 1 ratio, meaning AG : GE = 2 : 1, Check the picture below.

The rate of increase of the volume of the cube is 0.8 cubic inches per second.

Let x denote the edge of the cube at any given instant.

The total surface area of the cube

= 6x^2

The given condition is: 6x^2 = 150

=> x^2 = 25

=> x = 5

Now, the rate of increase of the edge of the cube is 0.2 inches/second.

Therefore, the rate of increase of the volume of the cube = rate of increase of the edge * rate of increase of the edge * rate of increase of the edge

=> 0.2 * 0.2 * 0.2

= 0.008 inches^3/second

= 0.8 cubic inches/second

The rate of increase of the volume of the cube is 0.8 cubic inches per second, which is calculated by multiplying the rate of increase of the edge (0.2 inches/second) three times.

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The completed statement using the integers that are closest to the number in the middle is 3<-√14<4

The statement: <-√14< can be interpreted as the set of all real numbers that are less than the square root of 14, which is approximately 3.74166.

The integers closest to this number are 3 and 4, so the set of integers that are closest to the number in the middle can be represented as:

(-∞, 3) U (4, ∞)

The statement says that the value of the square root of 14, when multiplied by -1 (the square root of a negative number), is between 3 and 4. The closest integers to the value of the square root of 14 are -3 and -4.

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======================================================

Explanation:

Check out the diagram below.

I've defined the following points:

Now focus on triangle ACF. This is an isosceles right triangle with legs of 0.5x each. The hypotenuse is the radius of the circle. Let R be that unknown radius.

The area of the circle is given to us. It is 56 square cm. Use this to find the value of R.

[tex]A = \pi*(\text{radius})^2\\\\56 = \pi*R^2\\\\R^2 = 56/\pi\\\\R = \sqrt{56/\pi}\\\\R = 4.22200825\\\\[/tex]

This value is approximate. I used the calculator's stored version of pi to get the most accuracy possible.

------------

We now know the hypotenuse of triangle ACF.

Use Pythagoras (aka Pythagorean Theorem) to have the following steps:

[tex]a^2+b^2 = c^2\\\\(0.5\text{x})^2+(0.5\text{x})^2 = 4.22200825^2\\\\0.25\text{x}^2+0.25\text{x}^2 = 17.82535366\\\\0.5\text{x}^2 = 17.82535366\\\\\text{x}^2 = 17.82535366/0.5\\\\\text{x}^2 = 35.65070732\\\\\text{x} = \sqrt{35.65070732}\\\\\text{x} = 5.97082132708726\\\\\text{x} = 5.97\\\\[/tex]

With the exception of 0.5 and 0.25, each decimal value mentioned is approximate.

Keep in mind that rounding to 3 sig figs means that we're rounding to 2 decimal places. The units digit is 1 sig fig, and the 2 decimal places give a total of 1+2 = 3 sig figs.

In short, we're rounding to the nearest hundredth.

--------------------

Check:

x = 5.97 is the square's side length.

It divides in half to get x/2 = 5.97/2 = 2.985 which gives each leg of triangle ACF.

Use a = 2.985 and b = 2.985 in the Pythagorean Theorem to find that c = 4.22142748 approximately. This is the approximate radius of the circle.

Use that radius to find the area of the circle.

A = pi*r^2

A = pi*(4.22142748)^2

A = 55.984594705958

A = 56.0

I'm rounding the area to 3 sig figs to keep consistent with the rounding done to x. We arrive at the circle area of 56 square cm, which helps confirm the answer is correct.

17297280 ways can the sites for the new stores be selected. This can be solved using the concept of probability.

The word "probability" derives from the Latin word "probitatem," which means "credibility, likelihood," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Given that,

14 different sites on which to locate 7 stores

For store 1, it can be placed on 14 sites.

Store 2 can be placed on 13 sites (since store 1 is already on site 1).

Store 3 can be placed on 12 sites and

so on until store 7 which has 8 sites.

Therefore the number of ways is:

C = 14 × 13 × 12 × 11 × 10 × 9 × 8

C = 17297280 ways

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A stable solution is a solution to a problem that does not change when the parameters of the problem are slightly varied. It is a point at which there is no net change, or a point of equilibrium.

A stable solution is a solution to a problem that does not change when the parameters of the problem are slightly varied. The parameters of a problem can refer to the data, assumptions, constraints, or other factors that are used to define the problem. When the parameters are changed, a stable solution will remain intact, indicating that it is the best solution to the problem.

For example, if a mathematics problem has a solution of 3, this solution is considered to be stable, as changing any of the parameters of the problem will not alter the solution of 3.

Stable solutions are important as they provide a point of equilibrium, or a point at which there is no net change. This can help to ensure that the solution is the most effective one to the problem.

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The equation of the transaction of friend 1 is; y = 0.12x + 30

The equation of the transaction of friend 2 is; y = 0.15x + 15

The general form if the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Friend 1;

Cost of the new phone including monthly fee = $30

Cost per 100 minutes = $12

Thus, cost per minute = 12/100 = $0.12 per minute

The cost per minute is simply the slope here while $30 is the y-intercept and as such the equation is;

y = 0.12x + 30

Friend 2;

Cost of the new phone including monthly fee = $15

Cost per 100 minutes = $15

Thus, cost per minute = 15/100 = $0.15 per minute

The cost per minute is simply the slope here while $15 is the y-intercept and as such the equation is;

y = 0.15x + 15

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